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Date:         Wed, 23 Oct 2002 11:26:49 -0500
Reply-To:     "Simon, Steve, PhD" <>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         "Simon, Steve, PhD" <>
Subject:      Re: design question (Non SPSS)
Comments: To: Tony Baglioni <>
Content-Type: text/plain

Tony Baglioni writes:

> I've forgotten so many basics. Can anyone tell me how to > calculate the needed sample size for a simple query? I > know the probability of an event is 3/10,000. What sample > size is needed to verify there are no cases present?

You need to be a bit more precise in your research hypothesis. If you already know the probability of an event, why are you running a test at all?

I'll make a guess that you want to find a sample large enough so that you can exclude the possibility that the true proportion is 3/10,000. In other words, you want to prove that the true proportion is less than 3/10,000.

The rule of three is helpful here. If you observe zero events out of n, then 3/n is an approximate 95% confidence interval for the true probability. Solve the equation

3/n < 0.0003

to get n > 10,000.

A more formal power calculation could be done, and it would probably demand an even larger sample size. You need to be more explicit with your hypothesis before you can do a power calculation. I understand that StatXact will do a power calculation for you, although I do not have the latest version which does this. The traditional formulas for power fall apart because the event is very rare.

Steve Simon,, Standard Disclaimer. The STATS web page has moved to

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